# Video: AQA GCSE Mathematics Foundation Tier Pack 3 • Paper 3 • Question 29

A number machine is shown. a) Calculate the output when the input is 9. b) Calculate the output when the input is −9.

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### Video Transcript

A number machine is shown. Part a) Calculate the output when the input is nine. Part b) Calculate the output when the input is negative nine.

The number machine has two steps to get from the input to the output, firstly subtracting one and secondly multiplying by four. In part a), we’re told that the input is nine. Subtracting one from nine gives us an answer of eight. Multiplying eight by four is 32. This means that when the input is nine, the output from the number machine is 32.

Part b) asks us to calculate the output when the input is negative nine. Subtracting one from negative nine gives us negative 10. Subtracting a number from a negative number takes us further down our number line. We then need to multiply negative 10 by four. Multiplying a negative number by a positive number gives us a negative answer. And 10 multiplied by four is equal to 40. Therefore, negative 10 multiplied by four is equal to negative 40. When the input to the number machine is negative nine, then its output is negative 40.

Whilst we are not asked to in this case, we could write the output 𝑦 as an expression in terms of the input 𝑥. The first step in our number machine is to subtract one. Therefore, we would have 𝑥 minus one. We then multiply this answer by four, 𝑥 minus one multiplied by four. This is usually written with a four in front of the bracket. So we have four multiplied by 𝑥 minus one. The output 𝑦 in this question is equal to four multiplied by 𝑥 minus one. We could then use this to work out the output when we are given any input 𝑥.